Now you take it or leave it.” For this to work, Ann must commit herself

credibly.

Aumann: In other words, it™s not enough for her just to say it. She

has to make it credible; and then Bob will rationally accept the 10. The

dif¬culty with this is that perhaps Bob, too, can credibly commit to

accepting no less than 90. So we have a paradox: once Ann credibly

commits herself to accepting no less than 90, Bob is rationally motivated

to take the 10. But then Ann is rationally motivated to make such a com-

mitment. But Bob could also make such a commitment; and if both make

the commitment, it is not rational, because then nobody gets anything.

An Interview with Robert Aumann 387

This is the blackmailer™s paradox. It is recognized in game theory,

therefore, that it is perhaps not so rational for the guy on the receiving

end of the threat to accept it.

What is the application of this to the situation we have here in Israel?

Let me tell you this true story. A high-ranking of¬cer once came to my

of¬ce at the Center for Rationality and discussed with me the situation

with Syria and the Golan Heights. This was a hot topic at the time. He

explained to me that the Syrians consider land holy, and they will not

give up one inch. When he told me that, I told him about the black-

mailer™s paradox. I said to him that the Syrians™ use of the term “holy,” land

being holy, is a form of commitment. In fact, they must really convince

themselves that it™s holy, and they do. Just like in the blackmailer™s paradox,

we could say that it™s holy; but we can™t convince ourselves that it is. One

of our troubles is that the term “holy” is nonexistent in our practical,

day-to-day vocabulary. It exists only in religious circles. We accept holi-

ness in other people and we are not willing to promote it on our own

side. The result is that we are at a disadvantage because the other side

can invoke holiness, but we have ruled it out from our arsenal of tools.

Hart: On the other hand, we do have such a tool: security considera-

tions. That is the “holy” issue in Israel. We say that security considera-

tions dictate that we must have control of the mountains that control

the Sea of Galilee. There is no way that anything else will be acceptable.

Throughout the years of Israel™s existence, security considerations have

been a kind of holiness, a binding commitment to ourselves. The question

is whether it is as strong as the holiness of the land on the other side.

Aumann: It is less strong.

Hart: Maybe that explains why there is no peace with Syria.

Aumann: You know, the negotiations that Rabin held with the Syrians

in the early nineties blew up over a few meters. I really don™t understand

why they blew up, because Rabin was willing to give almost everything

away. Hills, everything.

Without suggesting solutions, it is just a little bit of an insight into

how game-theoretic analysis can help us to understand what is going on,

in this country in particular, and in international con¬‚icts in general.

Hart: Next, what about what you refer to as “connections”?

Aumann: A lot of game theory has to do with relationships among

different objects. I talked about this in my 1995 “birthday” lecture, and

it is also in the Introduction to my Collected Papers [Aumann (2000)].

Science is often characterized as a quest for truth, where truth is

something absolute, which exists outside of the observer. But I view

science more as a quest for understanding, where the understanding is

388 Sergiu Hart

that of the observer, the scientist. Such understanding is best gained by

studying relations”relations between different ideas, relations between

different phenomena; relations between ideas and phenomena. Rather

than asking “How does this phenomenon work?” we ask, “How does

this phenomenon resemble others with which we are familiar?” Rather

than asking “Does this idea make sense?” we ask, “How does this idea

resemble other ideas?”

Indeed, the idea of relationship is fundamental to game theory. Dis-

ciplines like economics or political science use disparate models to analyze

monopoly, oligopoly, perfect competition, public goods, elections, coali-

tion formation, and so on. In contrast, game theory uses the same tools

in all these applications. The nucleolus yields the competitive solution in

large markets [Aumann (1964)], the homogeneous weights in parlia-

ments (cf., Peleg), and the Talmudic solution in bankruptcy games

[Aumann and Maschler (1985)]. The fundamental notion of Nash equi-

librium, which a priori re¬‚ects the behavior of consciously maximizing

agents, is the same as an equilibrium of populations that reproduce blindly

without regard to maximizing anything.

The great American naturalist and explorer John Muir said, “When

you look closely at anything in the universe, you ¬nd it hitched

to everything else.” Though Muir was talking about the natural universe,

this applies also to scienti¬c ideas”how we understand our universe.

Hart: How about the issue of assumptions versus conclusions?

Aumann: There is a lot of discussion in economic theory and in game

theory about the reasonableness or correctness of assumptions and

axioms. That is wrongheaded. I have never been so interested in assump-

tions. I am interested in conclusions. Assumptions don™t have to be correct;

conclusions have to be correct. That is put very strongly, maybe more

than I really feel, but I want to be provocative. When Newton intro-

duced the idea of gravity, he was laughed at, because there was no rope

with which the sun was pulling the earth; gravity is a laughable idea, a

crazy assumption, it still sounds crazy today. When I was a child I was

told about it. It did not make any sense then, and it doesn™t now; but it

does yield the right answer. In science one never looks at assumptions;

one looks at conclusions. It does not interest me whether this or that

axiom of utility theory, of the Shapley value, of Nash bargaining is or is

not compelling. What interests me is whether the conclusions are compel-

ling, whether they yield interesting insights, whether one can build useful

theory from them, whether they are testable. Nowhere else in science

does one directly test assumptions; a theory stands or falls by the validity

of the conclusions, not of the assumptions.

An Interview with Robert Aumann 389

Hart: Would you like to say something about the ethical neutrality of

game theory?

Aumann: Ethical neutrality means that game theorists don™t neces-

sarily advocate carrying out the normative prescriptions of game theory.

Game theory is about sel¬shness. Just like I suggested studying war,

game theory studies sel¬shness. Obviously, studying war is not the

same as advocating war; similarly, studying sel¬shness is not the same

as advocating sel¬shness. Bacteriologists do not advocate disease; they

study it. Game theory says nothing about whether the “rational” way is

morally or ethically right. It just says what rational”self-interested”

entities will do; not what they “should” do, ethically speaking. If we

want a better world, we had better pay attention to where rational incen-

tives lead.

Hart: That™s a very good conclusion to this fascinating interview.

Thank you.

Aumann: And thank you, Sergiu, for your part in this wonderful

interview.

REFERENCES

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374“392.

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In A.W. Tucker & R.D. Luce (eds.), Contributions to the Theory of Games IV,

Annals of Mathematics Study 40, pp. 287“324. Princeton, NJ: Princeton

University Press.

Aumann, R.J. (1961) The core of a cooperative game without side payments.

Transactions of the American Mathematical Society 98, 539“552.

Aumann, R.J. (1964) Markets with a continuum of traders. Econometrica 32,

39“50.

Aumann, R.J. (1965) Integrals of set-valued functions. Journal of Mathematical

Analysis and Applications 12, 1“12.

Aumann, R.J. (1966) Existence of competitive equilibria in markets with a con-

tinuum of traders. Econometrica 34, 1“17.

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In M. Shubik (ed.), Essays in Mathematical Economics in Honor of Oskar

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nal of Mathematical Economics 1, 67“96.

Aumann, R.J. (1975) Values of markets with a continuum of traders. Econometrica

43, 611“646.

Aumann, R.J. (1976) Agreeing to disagree. Annals of Statistics 4, 1236“1239.

390 Sergiu Hart